Finite Group Databasebeta

← Group #257016

Character table — Group #257016

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244442244444422244444444444444888888882444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-11-1-11111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-11-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-111111111111111111111-1-11-1-1-11-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-111111111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-111-1-11-1-1-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-111111-1-1-1-1
χ9111111111111-1-1-1-1-1-11-1-1111-111-1-111111111-1-1-1-11111-1-1-1-1-11-1-11-1-1111-1-111-1-1
χ10111111111111-1-1-1-1-1-11-1-1111-111-1-11111-1-1-1-11111-1-1-1-11111-11-1-11-1-11-1-111-1-111
χ11111111111111-1-1-1-1-1-11-1-1111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11-111-1-1-1-111
χ12111111111111-1-1-1-1-1-11-1-1111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11-1-1-11111-1-1
χ13111111111111-1-1-1-1-1-11-1-1111-1-1-11111111111-1-1-1-11111-1-1-1-11-1-11-11-1-1-1-111-1-111
χ14111111111111-1-1-1-1-1-11-1-1111-1-1-1111111-1-1-1-11111-1-1-1-111111-1-11-11-1-111-1-111-1-1
χ15111111111111-1-1-1-1-1-11-1-1111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-11111-1-11111-1-1
χ16111111111111-1-1-1-1-1-11-1-1111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1111111-1-1-1-111
χ172222222222222222-2-2-222-2-2-2-22222000000000000000000000-2000-20000000000
χ182222222222222222-2-2-222-2-2-2-2-2-2-2-2000000000000000000000200020000000000
χ19222222222222-2-2-2-222-2-2-2-2-2-2222-2-2000000000000000000000-200020000000000
χ20222222222222-2-2-2-222-2-2-2-2-2-22-2-2220000000000000000000002000-20000000000
χ2122222222-2-2-2-22222222-2-2-2-22-2000022-2-20000000000000000002000-2000000000
χ2222222222-2-2-2-22222222-2-2-2-22-20000-2-222000000000000000000-20002000000000
χ2322222222-2-2-2-22222-2-2-2-2-222-22000000000000000000000000200-2200-200000000
χ2422222222-2-2-2-22222-2-2-2-2-222-22000000000000000000000000-2002-200200000000
χ2522222222-2-2-2-2-2-2-2-222-22222-2-2000000000000000000000000200-2-200200000000
χ2622222222-2-2-2-2-2-2-2-222-22222-2-2000000000000000000000000-2002200-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222-2-222000022-2-2000000000000000000-20002000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222-2-2220000-2-2220000000000000000002000-2000000000
χ29222-22-2-2-22-22-2000000-2002-22000002i−2i2i−2i00002i2i−2i−2i000022-2-20000000000000000
χ30222-22-2-2-22-22-2000000-2002-22000002i−2i2i−2i0000−2i−2i2i2i0000-2-2220000000000000000
χ31222-22-2-2-22-22-2000000-2002-2200000−2i2i−2i2i00002i2i−2i−2i0000-2-2220000000000000000
χ32222-22-2-2-22-22-2000000-2002-2200000−2i2i−2i2i0000−2i−2i2i2i000022-2-20000000000000000
χ33222-22-2-2-2-22-22000000-200-222000002i−2i−2i2i2i2i−2i−2i000022-2-200000000000000000000
χ34222-22-2-2-2-22-22000000-200-222000002i−2i−2i2i−2i−2i2i2i0000-2-22200000000000000000000
χ35222-22-2-2-2-22-22000000-200-22200000−2i2i2i−2i2i2i−2i−2i0000-2-22200000000000000000000
χ36222-22-2-2-2-22-22000000-200-22200000−2i2i2i−2i−2i−2i2i2i000022-2-200000000000000000000
χ3722-22-2-22-22-2-222i2i−2i−2i0002i−2i00002-22i−2i0000000000002−22−2i2−i2i2−i20000000000002−2i2−i2
χ3822-22-2-22-22-2-222i2i−2i−2i0002i−2i00002-22i−2i000000000000−22−22−i2i2−i2i2000000000000−22−i2i2
χ3922-22-2-22-22-2-222i2i−2i−2i0002i−2i0000-22−2i2i0000000000002−22−2i2−i2i2−i2000000000000−22−i2i2
χ4022-22-2-22-22-2-222i2i−2i−2i0002i−2i0000-22−2i2i000000000000−22−22−i2i2−i2i20000000000002−2i2−i2
χ4122-22-2-22-22-2-22−2i−2i2i2i000−2i2i00002-2−2i2i0000000000002−22−2−i2i2−i2i20000000000002−2−i2i2
χ4222-22-2-22-22-2-22−2i−2i2i2i000−2i2i00002-2−2i2i000000000000−22−22i2−i2i2−i2000000000000−22i2−i2
χ4322-22-2-22-22-2-22−2i−2i2i2i000−2i2i0000-222i−2i0000000000002−22−2−i2i2−i2i2000000000000−22i2−i2
χ4422-22-2-22-22-2-22−2i−2i2i2i000−2i2i0000-222i−2i000000000000−22−22i2−i2i2−i20000000000002−2−i2i2
χ45444-44-4-4-44-44-4000000400-44-400000000000000000000000000000000000000000
χ46444-44-4-4-4-44-440000004004-4-400000000000000000000000000000000000000000
χ4744-44-4-44-4-444-44i4i−4i−4i000−4i4i00000000000000000000000000000000000000000000
χ4844-44-4-44-4-444-4−4i−4i4i4i0004i−4i00000000000000000000000000000000000000000000
χ4944-4-4-44-4444-4-40000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ5044-4-4-44-4444-4-4000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ5144-4-4-44-44-4-4440000000000000000000000000000022−22−222200000000000000000000
χ5244-4-4-44-44-4-44400000000000000000000000000000−222222−2200000000000000000000
χ534-444-4-4-4400004i−4i4i−4i000000000000000000000000000000000000000002-22i−2i0000
χ544-444-4-4-4400004i−4i4i−4i00000000000000000000000000000000000000000-22−2i2i0000
χ554-444-4-4-440000−4i4i−4i4i000000000000000000000000000000000000000002-2−2i2i0000
χ564-444-4-4-440000−4i4i−4i4i00000000000000000000000000000000000000000-222i−2i0000
χ574-4-4444-4-400004-4-44000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ584-4-4444-4-400004-4-4400000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ594-4-4444-4-40000-444-4000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ604-4-4444-4-40000-444-400000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ614-4-4-44-444000000004-40000000000000002-2-222-2-22000000000000000000000000
χ624-4-4-44-444000000004-4000000000000000-222-2-222-2000000000000000000000000
χ634-4-4-44-44400000000-440000000000000002-2-22-222-2000000000000000000000000
χ644-4-4-44-44400000000-44000000000000000-222-22-2-22000000000000000000000000
χ658-88-8-888-8000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).